Yang-Mills analogues of the Immirzi ambiguity

TL;DR

This paper explores analogies between the Immirzi ambiguity in quantum gravity and similar ambiguities in Yang-Mills and Maxwell theories, discussing their implications for loop quantization.

Contribution

It introduces a novel analogy between the Immirzi ambiguity and ambiguities in Yang-Mills theories, expanding understanding of quantum gravity ambiguities.

Findings

Identifies parallels between Immirzi and theta ambiguities

Discusses implications for loop quantum gravity

Analyzes ambiguities in Maxwell theory

Abstract

We draw parallels between the recently introduced ``Immirzi ambiguity'' of the Ashtekar-like formulation of canonical quantum gravity and other ambiguities that appear in Yang-Mills theories, like the $\theta$ ambiguity. We also discuss ambiguities in the Maxwell case, and implication for the loop quantization of these theories.